a P-recursive equation is a linear equation of sequences where the coefficient sequences can be represented as polynomials. P-recursive equations are...

In mathematics a P-recursive equation can be solved for polynomial solutions. Sergei A. Abramov in 1989 and Marko Petkovšek in 1992 described an algorithm...

A Bellman equation, named after Richard E. Bellman, is a necessary condition for optimality associated with the mathematical optimization method known...

solutions of linear difference equations with polynomial coefficients are called P-recursive. For these specific recurrence equations algorithms are known which...

are equations which define one or more sequences recursively. Some specific kinds of recurrence relation can be "solved" to obtain a non-recursive definition...

Recursive least squares (RLS) is an adaptive filter algorithm that recursively finds the coefficients that minimize a weighted linear least squares cost...

10  (also known as a linear recurrence relation or linear difference equation) sets equal to 0 a polynomial that is linear in the various iterates of...

primitive recursive function terminology": In the definition of ρ ( g , h ) {\displaystyle \rho (g,h)} , the first equation suggests to choose g = P 1 1 {\displaystyle...

on the Fresnel equations, but with additional calculations to account for interference. The transfer-matrix method, or the recursive Rouard method  can...

{\displaystyle s_{0},s_{1},s_{2},s_{3},\ldots } is called constant-recursive if it satisfies an equation of the form s n = c 1 s n − 1 + c 2 s n − 2 + ⋯ + c d s...

Pell's equation, also called the Pell–Fermat equation, is any Diophantine equation of the form x 2 − n y 2 = 1 , {\displaystyle x^{2}-ny^{2}=1,} where...

is sometimes represented in what is called an Euler equation. A time-series path in the recursive model is the result of a series of these two-period...

solutions to smaller instances of the same problem. Recursion solves such recursive problems by using functions that call themselves from within their own...

Bethe–Salpeter equation appears in many forms. One form often used in high energy physics is Γ ( P , p ) = ∫ d 4 k ( 2 π ) 4 K ( P , p , k ) S ( k − P 2 ) Γ ( P ,...

 2, 1 can be found by working backwards, using a recursive relationship called the Bellman equation. For i = 2, ..., n, Vi−1 at any state y is calculated...

Lane-Emden equation, we can show that all odd coefficients of the series vanish a 2 m + 1 = 0 {\displaystyle a_{2m+1}=0} . Furthermore, we obtain a recursive relationship...

corresponding equation. The unsolvability of Hilbert's tenth problem is a consequence of the surprising fact that the converse is true: Every recursively enumerable...

{-c}{x}}\\x&=-b-{\frac {c}{x}}\,\end{aligned}}} But now we can apply the last equation to itself recursively to obtain x = − b − c − b − c − b − c − b − c − b − ⋱ {\displaystyle...

{\displaystyle S(0)=0} is a negated proposition. Further, recursive defining equations for every primitive recursive function may be adopted as axioms as desired....

Pergamon Press 1963, Dover 2007 Recursive number theory - a development of recursive arithmetic in a logic-free equation calculus, North Holland 1957 Constructive...

ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is...

differential equation of the form d d x [ p ( x ) d y d x ] + q ( x ) y = − λ w ( x ) y {\displaystyle {\frac {\mathrm {d} }{\mathrm {d} x}}\left[p(x){\frac...

form of a stochastic difference equation (or recurrence relation) which should not be confused with a differential equation. Together with the moving-average...

Consider a problem that can be solved using a recursive algorithm such as the following: procedure p(input x of size n): if n < some constant k: Solve...

defined recursively by P 1 = ϕ , P n = − d P n − 1 d x + ∑ i = 1 n − 2 P i P n − 1 − i  for  n ≥ 2. {\displaystyle {\begin{aligned}P_{1}&=\phi ,\\P_{n}&=-{\frac...

;\delta t)={\vec {0}}.} In the equation-free context, the recursive projection method is the outer solver of this equation, and the coarse time-stepper...

number with a given property. Adding the μ-operator to the primitive recursive functions makes it possible to define all computable functions. Suppose...

results in the following recursive equations for P k ∣ k a {\displaystyle \mathbf {P} _{k\mid k}^{a}}  : P k ∣ k − 1 a = F k P k − 1 ∣ k − 1 a F k T +...

A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves derivatives...

theory. The renewal function satisfies a recursive integral equation, the renewal equation. The key renewal equation gives the limiting value of the convolution...